Locus of centroid of the triangle whose vertices are \[(\alpha cos\,t,a\,sin\,t),(b\,sin\,t,-b\,cos\,t)\] and \[(1,0)\], where t is a parameter, is

\[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

\[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

\[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

\[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

Locus of centroid of the triangle whose vertices are \[(\alpha cos\,t,

1.	Locus of centroid of the triangle whose vertices are \[(\alpha cos\,t,a\,sin\,t),(b\,sin\,t,-b\,cos\,t)\] and \[(1,0)\], where t is a parameter, is
A.	\[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
B.	\[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
C.	\[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
D.	\[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
Answer» D. \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

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Locus of centroid of the triangle whose vertices are \[(\alpha cos\,t,a\,sin\,t),(b\,sin\,t,-b\,cos\,t)\] and \[(1,0)\], where t is a parameter, is

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